\(\left(x-1\right)^5=\left(x-1\right)^{15}\)
\(\Rightarrow\left(x-1\right)^5-\left(x-1\right)^{15}=0\)
\(\Rightarrow\left(x-1\right)^5.\left[1-\left(x-1\right)^{10}\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-1\right)^5=0\\1-\left(x-1\right)^{10}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-1=0\\\left(x-1\right)^{10}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0+1\\x-1=1\\x-1=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=1+1\\x=\left(-1\right)+1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=2\\x=0\end{matrix}\right.\)
Vậy \(x\in\left\{1;2;0\right\}.\)
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